please use python to answer the question

Write a program to compute an approximate value for the derivative of a function using the finite-difference formula f'(x) ~ f(x + h) - f(x)/h. Test your program using the function sin(x) for x = 1. Determine the error by comparing with the built-in function cos(x). Plot the magnitude of the error as a function of h, for h = 1/2, 1/4, 1/8, ... You should use a log scale for h and for the magnitude of the error. Is there a minimum value for the magnitude of the error? How does the corresponding value for h compare with the rule of thumb h ~ Squareroot _mach middot |x|? (b) Repeat the exercise using the centered difference approximation f'(x) ~ f(x + h) - f(x - h)/2h